Counting fermionic zero modes on M5 with fluxes

TL;DR

This paper investigates how background fluxes influence fermionic zero modes on M5 branes in Calabi-Yau fourfolds, revealing flux-dependent solutions that affect anomaly calculations and instanton contributions to the superpotential.

Contribution

It introduces a method to count fermionic zero modes via a finite-dimensional linear system affected by fluxes, linking flux choices to anomaly and superpotential corrections.

Findings

Flux alters the fermionic zero mode count.

Presence of flux enables instanton corrections.

Method simplifies anomaly computation on M5 branes.

Abstract

We study the Dirac equation on an M5 brane wrapped on a divisor in a Calabi--Yau fourfold in the presence of background flux. We reduce the computation of the normal bundle U(1) anomaly to counting the solutions of a finite--dimensional linear system on cohomology. This system depends on the choice of flux. In an example, we find that the presence of flux changes the anomaly and allows instanton corrections to the superpotential which would otherwise be absent.